What is the order of the differential equation given below?
2
4
3
2
6
3
2
2
d y
x
x
x
dx
Options:
(A) 1
(B) 2
(C) 3
(D) 4
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2022 Q.11)**
**1. Governing Concept**:
- **Topic**: Engineering Mathematics & Differential Equations
- The **order** of a differential equation is the order of the highest derivative appearing in the equation.
- The **degree** is the power of the highest derivative (after removing fractional/radical powers).
- The given differential equation contains a second derivative $\frac{d^2 y}{dx^2}$ as its highest derivative term, making its order **2**.
**2. Option Analysis**:
- **Option (A) [1] is INCORRECT**: First-order involves only $\frac{dy}{dx}$.
- **Option (B) [2] is CORRECT**: The highest derivative order in the equation is 2.
- **Option (C) [3] is INCORRECT**: No third-order derivative present.
- **Option (D) [4] is INCORRECT**: No fourth-order derivative present.
**3. Final Answer**:
- **Correct Choice**: **B**
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